Let the edges of the rectangular parallelepiped be a, b and c.

Diagonals of the three faces meeting at a corner are:
√(a² + b²) = √5
√(b² + c²) = √10
√(c² + a²) = √13

Squaring:
a² + b² = 5 ...(1)
b² + c² = 10 ...(2)
c² + a² = 13 ...(3)

Adding (1), (2), (3):
2(a² + b² + c²) = 28

a² + b² + c² = 14

From (1): a² + b² = 5

So c² = 14 − 5 = 9 ⇒ c = 3

From (2): b² + 9 = 10 ⇒ b² = 1 ⇒ b = 1

From (1): a² + 1 = 5 ⇒ a² = 4 ⇒ a = 2

Volume = a × b × c = 2 × 1 × 3 = 6 cm³.

Thus, correct volume is 6 cm³.